"Last time I mentioned to you that charge resides at the surface of solid conductors but that it's not uniformly distributed. Perhaps you remember that, unless it happens to be a sphere.

And I want to pursue that today. If I had a solid conductor which say had this shape and I'm going to convince you today that right here the surface charge density will be higher than there. Because the curvature is stronger than it is here. And the way I want to approach that is as follows. Suppose I have here a solid conductor A which has radius R of A and very very far away, maybe tens of meters away, I have a solid conductor B with radius R of B and they are connected through a conducting wire.

That's essential. If they are connected through a conducting wire, then it's equipotential. They all have the same potential. I'm going to charge them up until I get a charge distribution QA here and I get QB there. The potential of A is about the same that it would be if B were not there..."